Authenitication of physical object using internal structure

ABSTRACT

A method for preventing counterfeiting of an object (e.g. paper) is described. The method comprises capturing an image of at least a portion of the object, wherein the portion of the object whose image is captured is at least partially transparent, and wherein the captured image includes features of the internal structure of the object (e.g. the texture of the paper resulting from the arrangement of fibres from which the paper is made). The method further comprises generating, based on the image, a code that encodes features of the internal structure of the object, and recording the code. Generating the code may comprise applying a filter to the image to obtain a filtered image, and processing the filtered image to obtain a binary code. The filter may be a Gabor filter, and processing the filtered image may comprise applying a Gray code to the filtered image. The method may further comprise encrypting the binary code, and recording the code may comprise recording the encrypted binary code. A method for authenticating an object is also described. The method comprises capturing an image of at least a portion of the object, wherein the portion of the object whose image is captured is at least partially transparent, and wherein the captured image includes features of the internal structure of the object. The method further comprises generating, based on the image, a code that encodes features of the internal structure of the object, reading one or more reference values comprising at least a reference code, and authenticating the object based on the code and the reference code.

FIELD OF THE DISCLOSURE

Certain examples of the present disclosure provide a technique forauthenticating a physical object and/or for preventing cloning orcounterfeiting of a physical object. For example, the present disclosureprovides a technique for authenticating a physical object using theinternal structure of the object. Certain examples provide a techniquefor authenticating a piece of paper (e.g. a banknote) using the inherenttexture of the paper.

BACKGROUND

Designing secure documents (e.g. paper documents) that provide highlevels of security against physical forgery is a long-standing problem.Even in today's digital age, this problem remains important as physicalpaper is still prevalently used in our daily lives as a means to provedata authenticity, for example, in receipts, contracts, certificates,and passports. A recent trend in this area (e.g., in e-passports) is toembed electronics such as RFID chips within the physical document inquestion. However, the security of such solutions depends on thetamper-resistance of the chip which must securely store a long-termsecret. This tamper-resistance requirement can significantly increasethe cost of production. In view of the importance of ensuring theauthenticity of paper documents, researchers have been exploringapplying digital technologies to prevent counterfeiting.

The above information is presented as background information only toassist with an understanding of the present disclosure. No determinationhas been made, and no assertion is made, as to whether any of the abovemight be applicable as prior art with regard to the present disclosure.

SUMMARY

It is an aim of certain examples of the present disclosure to address,solve, mitigate or obviate, at least partly, at least one of theproblems and/or disadvantages associated with the related art, forexample at least one of the problems and/or disadvantages mentionedherein. Certain examples of the present disclosure aim to provide atleast one advantage over the related art, for example at least one ofthe advantages mentioned herein.

Certain examples of the present disclosure are defined by theindependent claims. A non-exhaustive set of advantageous features thatmay be used in various examples of the present disclosure are defined inthe dependent claims.

In accordance with an aspect of the present disclosure, there isprovided a method for preventing counterfeiting of an object, the methodcomprising: capturing an image of at least a portion of the object,wherein the portion of the object whose image is captured is at leastpartially transparent, and wherein the captured image includes featuresof the internal structure of the object; generating, based on the image,a code that encodes features of the internal structure of the object;and recording the code.

In accordance with another aspect of the present disclosure, there isprovided an apparatus for preventing counterfeiting of an object, theapparatus comprising: a camera for capturing an image of at least aportion of the object, wherein the portion of the object whose image iscaptured is at least partially transparent, and wherein the capturedimage includes features of the internal structure of the object; aprocessor for generating, based on the image, a code that encodesfeatures of the internal structure of the object, and outputting thecode.

In accordance with another aspect of the present disclosure, there isprovided a method for authenticating an object, the method comprising:capturing an image of at least a portion of the object, wherein theportion of the object whose image is captured is at least partiallytransparent, and wherein the captured image includes features of theinternal structure of the object; generating, based on the image, a codethat encodes features of the internal structure of the object; readingone or more reference values comprising at least a reference code; andauthenticating the object based on the code and the reference code.

In accordance with another aspect of the present disclosure, there isprovided an apparatus for authenticating an object, the apparatuscomprising: a camera for capturing an image of at least a portion of theobject, wherein the portion of the object whose image is captured is atleast partially transparent, and wherein the captured image includesfeatures of the internal structure of the object; a reader for readingone or more reference values comprising at least a reference code; aprocessor for generating, based on the image, a code that encodesfeatures of the internal structure of the object, and authenticating theobject based on the code and the reference code.

In certain examples, generating the code comprises: applying a filter tothe image to obtain a filtered image; and processing the filtered imageto obtain a binary code.

In certain examples, the filter is a Gabor filter.

In certain examples, the filtered image C(x, y) is given by:

C(x,y)=I(x,y)*G(x,y)=∫∫I(x,y)G(x−η,y−ξ)dηdξ

where I(x, y) represent the image in grey-scale using Cartesiancoordinates, C(x, y) is a complex number for each x and y, * denotesconvolution, and G(x, y) is the Gabor filter defined by:

${G\left( {x,y} \right)} = {\frac{f^{2}}{\pi\eta\gamma} \cdot {\exp \left( \frac{{\eta^{2}x^{\prime 2}} + {\gamma^{2}y^{\prime 2}}}{2\sigma^{2}} \right)} \cdot {\exp \left( {2\pi \; {ifx}^{\prime}} \right)}}$for  x^(′) = x cos (θ) + y sin (θ)  and  y^(′) = −x sin (θ) + y cos (θ)

where f is the frequency of the sinusoidal wave, η and γ are constantfactors that together determine the spatial ellipticity of the Gaborwavelet, θ represents the orientation of the ellipticity, and σ is thestandard deviation of the Gaussian envelope.

In certain examples, processing the filtered image comprises applying aGray code to the filtered image.

In certain examples, the Gray code is a two-bit Gray code for convertinga complex number a+bi into two bits based on which quarter of thecomplex plane the complex number falls in, applying the Gray codecomprises converting each element of the matrix C(x, y) into two bitsaccording to the Gray code, and C(x, y) represents the filtered image.

In certain examples, the method further comprises encrypting the binarycode, and recording the code comprises recording the encrypted binarycode.

In certain examples, the method further comprises: generating a randomkey, k; obtaining a codeword f_(p) by applying an error-correctionencoding scheme, ErrorCC, to the random key according tof_(p)=ErrorCC(k), wherein f_(p) has the same size as the binary codef_(a); computing an encrypted binary code according to r=f_(a)⊕f_(p),where ⊕ denotes modulo-2 addition; and computing a hash value accordingto h=H(k), where H is a one-way hash function, wherein recording thecode comprises recording r and h.

In certain examples, the method further comprises computing a digitalsignature, s, based on r and h, and recording the code comprisesrecording the digital signature.

In certain examples, the method further comprises: identifying adesignated area of the captured image from which the code is generated;and correcting the captured image for any rotational and/or linearmisalignment.

In certain examples, the designated area is indicated by a boundary, anda marker is provided at a predetermined position relative to thedesignated area for indicating a correct orientation of the designatedarea.

In certain examples, the method further comprises: identifying one ormore artefacts in the captured image; and generating a mask for theimage for masking the artefacts.

In certain examples, the method further comprises: illuminating one sideof the object; and capturing the image from the other side of theobject.

In certain examples, recording the code comprises one or more of:printing the code on the object; printing the code on the object in theform of a barcode or QR code; storing the code in a database; storingthe code on a recording medium that is readable via short-range wirelesscommunication; and storing the code on an electronically readablerecording medium.

In certain examples, the object comprises paper, and the internalstructure of the object comprises the texture of the paper resultingfrom the arrangement of fibres from which the paper is made.

In certain examples, the apparatus further comprises a light source forilluminating the portion of the object whose image is captured.

In certain examples, the reference values further comprise a referencehash value, and authenticating the object comprises: computing acodeword f_(p)′ according to f_(p)′=f_(s)⊕r, where f_(s) denotes thecode, r denotes the reference code, and ⊕ denotes modulo-2 addition;applying an error correction code scheme to the codeword f_(p)′ toobtain a value k′; authenticating the object based on a comparisonbetween a hash value computed from the value k′ and the reference hashvalue.

In certain examples, the method further comprises verifying the one ormore reference values based on a digital signature of the one or morereference values.

In accordance with another aspect of the present disclosure, there isprovided a computer program comprising instructions arranged, whenexecuted, to implement a method, device, apparatus and/or system inaccordance with any aspect, embodiment, example or claim disclosedherein. In accordance with another aspect of the present disclosure,there is provided a machine-readable storage storing such a program.

Certain examples of the present disclosure provide a paperfingerprinting technique based on analyzing the translucent patternsrevealed when a light source shines through the paper. These patternsrepresent the inherent texture of paper, formed by the randominterleaving of wooden particles during the manufacturing process. Thesepatterns can be captured, for example, by a commodity camera andcondensed, for example into a compact 2048-bit fingerprint code. Certainalternative techniques focus on fingerprinting paper based on the paper“surface”. However, capturing the surface alone may miss importantdistinctive features such as the non-even thickness, the randomdistribution of impurities, and different materials in the paper withvarying opacities. On the other hand, the embedded paper texture mayprovide a more reliable source for fingerprinting than features on thesurface. Certain examples of the present disclosure may achieve 0% falserejection and 0% false acceptance rates. In certain examples, extractedfingerprints may contain 807 degrees-of-freedom (DoF), which is muchhigher than the 249 DoF with iris codes (that have the same size of 2048bits). The high amount of DoF for texture-based fingerprints makescertain examples of the present disclosure extremely scalable forrecognition among very large databases; it also allows secure usage ofthe extracted fingerprint in privacy-preserving authentication schemesbased on error correction techniques.

Other aspects, advantages, and salient features of the presentdisclosure will become apparent to those skilled in the art from thefollowing detailed description, which, taken in conjunction with theaccompanying drawings, disclose examples of the present disclosure.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates the surface and texture of the same area of a papersheet as captured by a camera based on a) reflective and b) transmissivelight;

FIG. 2 illustrates a step-by-step rotation recognition process in thepreparation phase of an example of the present disclosure;

FIG. 3 illustrates a Gray code for a complex value m_(ij)=a+bi in thecomplex plain;

FIG. 4 illustrates an exemplary implementation according to the presentdisclosure;

FIG. 5 illustrates capturing a photo, in case of (a) transmission, and(b) reflection, using the same digital camera and light source;

FIG. 6 illustrates Hamming distance distributions for surface andtexture;

FIG. 7 illustrates results of (a) decidability and (b) degrees offreedom in scales 1 to 7 and orientations 1 to 8;

FIG. 8 illustrates Hamming distance distributions in a benchmarkdataset;

FIG. 9 illustrates histograms of Hamming distances in the benchmarkdataset;

FIG. 10 illustrates a captured photo under near-ideal and non-idealsituations;

FIG. 11 illustrates Hamming distance distributions for robustnessexperiments;

FIG. 12 illustrates distributions of Hamming distances for a light boxexperiment;

FIG. 13 illustrates a generated QR Code in an authentication protocol,where the QR code contains the encrypted fingerprint, H(k) and a digitalsignature for both items;

FIG. 14 illustrates histogram of Hamming distances between rawfingerprints without masks;

FIGS. 15 and 16 are respectively a flow chart of a method, and a blockdiagram of an apparatus, for preventing counterfeiting of an objectaccording to examples of the present disclosure; and

FIGS. 17 and 18 are respectively a flow chart of a method, and a blockdiagram of an apparatus, for authenticating an object according toexamples of the present disclosure.

DETAILED DESCRIPTION OF EXAMPLES OF THE DISCLOSURE

The following description of examples of the present disclosure, withreference to the accompanying drawings, is provided to assist in acomprehensive understanding of the present invention, as defined by theclaims. The description includes various specific details to assist inthat understanding but these are to be regarded as merely exemplary.Accordingly, those of ordinary skill in the art will recognize thatvarious changes and modifications of the examples described herein canbe made without departing from the scope of the present invention, asdefined by the claims.

The terms and words used in this specification are not limited to thebibliographical meanings, but, are merely used to enable a clear andconsistent understanding of the present disclosure.

The same or similar components may be designated by the same or similarreference numerals, although they may be illustrated in differentdrawings.

Detailed descriptions of elements, features, components, structures,constructions, functions, operations, processes, characteristics,properties, integers and steps known in the art may be omitted forclarity and conciseness, and to avoid obscuring the subject matter ofthe present disclosure.

Throughout this specification, the words “comprises”, “includes”,“contains” and “has”, and variations of these words, for example“comprise” and “comprising”, means “including but not limited to”, andis not intended to (and does not) exclude other elements, features,components, structures, constructions, functions, operations, processes,characteristics, properties, integers, steps and/or groups thereof.

Throughout this specification, the singular forms “a”, “an” and “the”include plural referents unless the context dictates otherwise. Forexample, reference to “an object” includes reference to one or more ofsuch objects.

By the term “substantially” it is meant that the recited characteristic,parameter or value need not be achieved exactly, but that deviations orvariations, including for example, tolerances, measurement errors,measurement accuracy limitations and other factors known to those ofskill in the art, may occur in amounts that do not preclude the effectthe characteristic, parameter or value was intended to provide.

Throughout this specification, language in the general form of “X for Y”(where Y is some action, process, function, activity, operation or stepand X is some means for carrying out that action, process, function,activity, operation or step) encompasses means X adapted, configured orarranged specifically, but not exclusively, to do Y.

Elements, features, components, structures, constructions, functions,operations, processes, characteristics, properties, integers, stepsand/or groups thereof described herein in conjunction with a particularaspect, embodiment, example or claim are to be understood to beapplicable to any other aspect, embodiment, example or claim disclosedherein unless incompatible therewith.

It will be appreciated that examples of the present disclosure can berealized in the form of hardware, software or any combination ofhardware and software. Any such software may be stored in any suitableform of volatile or non-volatile storage device or medium, for example aROM, RAM, memory chip, integrated circuit, or an optically ormagnetically readable medium (e.g. CD, DVD, magnetic disk or magnetictape). It will also be appreciated that storage devices and media areexamples of machine-readable storage that are suitable for storing aprogram or programs comprising instructions that, when executed,implement examples of the present disclosure.

One technique to prevent counterfeiting is based on measuring the uniquephysical properties of paper that are very difficult or impossible toclone.

Manufacturing a paper sheet is a complex process and each paper sheet isa unique product from that process. Typically, wooden particles are usedas the base, and multiple substances are subsequently applied to stickthese particles together to stabilize their placement and shape a thin,usually white, steady surface which we call paper.

The surface of a paper sheet is imperfect—it contains randomnon-evenness as a natural outcome of the paper manufacturing process.The surface imperfections may be utilized to uniquely identify thepaper. In one approach, a focused laser beam may be used to scan apre-designated region on the paper sheet from four different angles, andthe intensity of the reflected laser may be continuously recorded. Therecordings then constitute a unique digital representation of the paper,which may be called a “paper fingerprint”.

A commodity scanner may be used to effectively extract paperfingerprints based on the same surface imperfections. A possible methodis to scan the paper surface from four different angles and thenconstruct a 3-D model. Then the 3-D model is condensed into a concisefeature vector, which forms the paper fingerprint.

Another approach uses a microscope with a built-in LED as the lightsource to extract the paper speckle patterns at the microscopic level(e.g. 1-2 microns). This approach is based on the concept of speckles:i.e., when light falls on a paper sheet, the scattered light formsrandomly mixed bright and dark regions, which can then be captured by amicroscope. The captured image can be further processed to produce acompact binary fingerprint.

Certain techniques focus on the imperfections of the paper surface. Incontrast, the wooden particles constituting the building blocks of apaper sheet scatter over the paper quite irregularly, and in certainexamples of the present disclosure, this irregular placement of woodenparticles provides a unique pattern, which can be extracted and used asa paper fingerprint. The unique pattern caused by the randominterleaving of wooden particles may be referred to as the texture ofpaper.

Unlike techniques that measure the paper surface characteristics,certain examples of the present disclosure fingerprint a paper sheetbased on measuring the paper texture patterns. The texture may becaptured, for example by putting a light source on one side of the paperand using a commodity camera to take a photograph on the other side.This is based on the observation that putting a paper sheet under lightwill reveal irregular textural patterns, which may be visible even tothe naked eye. FIG. 1 shows the difference between photos taken of thepaper surface (based on reflective light) and of the paper texture(based on transmissive light).

The following description discloses certain aspects of paperfingerprinting, and certain exemplary techniques using the texturalpatterns revealed by passing light through a paper sheet as a reliablesource for extracting a fingerprint (as opposed to measures which arebased on paper surface imperfections). In addition, the followingdescription discloses an exemplary paper fingerprinting algorithm basedon error correction and image processing techniques, and results ofexperiments to show that such an algorithm can be used to efficientlyextract a reliable and unique fingerprint using a photo taken by anoff-the-shelf camera. Certain examples of the present disclosure arefeasible and inexpensive to deploy in practice. In addition, thefollowing description discloses further experiments to demonstrate thatcertain examples of the present disclosure are robust against: (a)non-ideal photo capturing settings such as when the paper is rotated andthe light source is changed, and (b) non-ideal paper handling situationssuch as crumpling, soaking, heating and scribbling on the surface.

The skilled person will appreciate that the techniques describes hereinare not limited to paper, but may be applied to any suitable physicalobject (e.g. an object that is at least partially transparent and/orthat includes a detectable internal structure). In addition, the skilledperson will appreciate that the specific implementations disclosedherein are merely exemplary, and that that various modifications may bemade thereto without departing from the scope of the present disclosure.For example, in various examples one or more non-essential features(e.g. components, operations and/or method steps) may be omitted, and/orone or more optional features (e.g. components, operations and/or methodsteps) may be added. In addition, one or more feature (e.g. components,operations and/or method steps) may be replaced with equivalent orcomparable features, or features for performing an equivalent orcomparable function.

Paper Texture

When light falls on an object, it is partly absorbed, partly reflected,and partly transmitted, and paper is no exception. Absorption occursbased on the resonance principle: the energy of the light waves of aspecific frequency is absorbed and transformed into kinetic energy byelectrons of the same frequency. The part that is not absorbed, iseither reflected or transmitted depending on how opaque (or converselytransparent) the paper is.

Different types of paper behave differently in terms of how much lightthey absorb, reflect or transmit. This behaviour depends, among otherfactors, on pulp material, density, thickness and coating substances.Opacity, as defined by the ISO 2471 standard (ISO. 2008. Paper and boardDetermination of opacity (paper backing) Diffuse reflectance method. ISO2471:2008. International Organization for Standardization, Geneva,Switzerland), the entire contents of which are incorporated herein byreference, can be seen as an indicator of how much light is impeded fromtransmitting through the paper, with the opacity of 100% defined forfully opaque papers. Typical office printing paper, with grammagebetween 75 to 105 g/m², has opacity between 86% to 94%. To put this inperspective, opacity for newsprint paper (typical grammage: 40-49 g/m²)is in the range 90-94% and for tracing paper (typical grammage: 60-110g/m²) is in the range 24-40%. These values suggest that a considerableproportion of light transmits through such paper, which forms the basisof our proposal to fingerprint paper based on its textural patterns.

Intuitively, the textural patterns created and stabilized throughout thepaper in the process of manufacturing can provide a promising source forpaper fingerprinting. These patterns are naturally occurring and appearrandom. Moreover, they are embedded within the bonded structure of thepaper and hence are relatively well-protected against manual handling ofpaper. They are generated as a result of the wooden particles randomlyinterleaved during the manufacturing process. Finally, once in thefinished product, the randomly interleaved wooden particles cannot bealtered without damaging the paper, hence making any tampering actevident.

In certain examples, to capture the embedded textural patterns of paperand subsequently extract a fingerprint, a single photo may be taken, forexample by a commodity camera. This provides a more practical andquicker solution than other techniques that have to take multiple scans(e.g. on paper surface), for example from four different angles, inorder to compute a fingerprint. A single photo is feasible in certainexamples of the present disclosure because the paper texture typicallycontains richer features than the paper surface, such as the thicknessof the overlaying wooden particles, randomly distributed impurities, anddifferent embedded materials with varying opacities. The results ofexperiments descried below show that a paper fingerprint can be reliablyextracted from the textural patterns.

Examples of the present disclosure are applicable to a wide range ofobjects (e.g. paper objects). For example, a vast number of official andlegal documents, certificates, official receipts and invoices areprinted on regular office paper (sometimes with watermarks, holograms orother security measures), thermal paper, or other types of paper. Aproperty that the majority of these types of paper have in common isthat they are not completely opaque. This means that a considerableamount of light passes through them. Furthermore, embedded irregulartextural patterns as a natural result of the manufacturing process seemto be a universal property of all these different types of paper.Consequently, there is considerable potential for exploiting paperfingerprints extracted from embedded textural patterns in order tovalidate the authenticity of such official and legal documents.

Texture Analysis

A high level description of an example of the present disclosure forcapturing paper textural patterns and extracting a reliable and uniquepaper fingerprint from those patterns will now be described. To be ableto capture paper textural patterns, a digital photograph is taken of thepaper sheet through which light is projected. Then, a series ofpreparation operations are performed such as aligning and resizing ofthe original image. Afterwards, in the texture analysis phase, a 2-DGabor filter (for example, as described in John G Daugman. 1985.Uncertainty relation for resolution in space, spatial frequency, andorientation optimized by two-dimensional visual cortical filters. JOSA A2, 7 (1985), 1160-1169, the entire contents of which are incorporatedherein by reference) is utilized to extract textural information fromthe captured image. The skilled person will appreciate that examples ofthe present disclosure are not limited to a Gabor filter, and that anyother suitable type of filter or function may be used. Subsequently, apaper fingerprint extraction method is used that generates a binarystring, the paper fingerprint. Once paper fingerprints are in the binarystring format, they can be compared using any suitable method, such ascomputing the fractional Hamming distance between any two paperfingerprints.

The preparation phase, Gabor transform, the fingerprint generationmethod, and the fingerprint comparison method based on fractionalHamming distance will be described in more detail further below. Inaddition, further implementation details and settings of experimentswill be discussed further below.

Preparation Phase

The preparation phase comprises operations of identifying the designatedarea of the photo which is to be used for fingerprint extraction andaligning the image in terms of movement and rotation. To indicate thefingerprinting area, a small rectangular box may be printed on the papersheet. In addition, a filled square may be printed on the bottom left ofthe box, to allow automatic alignment.

FIG. 2 illustrates a step-by-step rotation recognition process in thepreparation phase of an example of the present disclosure. The last stepproduces a mask that distinguishes the pixels containing reliableinformation suitable for feature extraction (black region) from thepixels containing unreliable information (white region).

As shown in FIG. 2, aligning the rotation of the image involves severalsteps. First, a photo of the fingerprinting area is obtained. The photomay be converted into grey scale. The printed region (the rectangularbox and the filled square) can be identified by applying a grey-scalethreshold. This threshold may be computed, for example, by the Otsumethod (see, for example, Nobuyuki Otsu. 1975. A threshold selectionmethod from gray-level histograms. Automatica 11, 285-296 (1975), 23-27,the entire contents of which are incorporated herein by reference),which chooses the threshold in a such way to minimize the interclassvariance of black and white pixels. The same approach may be applied forboth reflection and transmission analyses. The borders in bothreflection and transmission samples may be recognized correctly usingthis technique. The result is a binary image: “0” for black and “1” forwhite. This thresholding may also produce some “noise” scattered aroundthe image, but they can be removed based on area. To ensure the bordersof the printed rectangle are connected, a convex hull of the outerpixels may be drawn to form a connected shape. This process alsoidentifies artefacts, e.g., caused by pen scribbling (which are testesin the robustness experiments described below). The pixel positions ofidentified artefacts may be defined in a mask function, which areexplained below.

Once the printed rectangle is identified, the region within therectangular border may be filled up with the binary value ‘1’ (white).The centre of the rectangular object may be identified. For example, the“centre of mass” of the object may be identified based on computing thefirst-order moment (for example, see Michael Reed Teague. 1980. Imageanalysis via the general theory of moments*. JOSA 70, 8 (1980), 920-930,the entire contents of which are incorporated herein by reference) anduse that as the new origin of the Cartesian coordinate system. Thiscorrects any misalignment due to paper movement.

Then, any misalignment caused by rotation may be corrected. This may bedone based on computing second-order moments in the new Cartesiancoordinate system (for example, see the Teague 1980 reference above).Let B(x, y) denote the binary 2D object in Cartesian coordinatesrepresenting the recognized rectangular box area. There are threesecond-order moments as follows:

u ₂₀ =∫∫x ² B(x,y)dxdy

u ₁₁ =∫∫xyB(x,y)dxdy

u ₀₂ =∫∫yB(x,y)dxdy

The rotation of the binary 2D object B(x, y) can now be calculated asfollows:

$\begin{matrix}{\theta = {\frac{1}{2}{\tan^{- 1}\left( \frac{2u_{11}}{\left( {u_{20} - u_{02}} \right) + \sqrt{\left( {u_{02} - u_{20}} \right)^{2} + {4u_{11}^{2}}}} \right)}}} & (1)\end{matrix}$

The above formula calculates the angle between the x axis and the majoraxis of an ellipse that has equal second moments to the recognizedrectangular box. It gives the counter-clockwise rotation of the objectwith respect to the horizon. After e is calculated, the image can berotated accordingly.

In the captured image, the borders of the rectangles may be slightlycurved rather than being straight due to lens artefact. This slightcurvature does not affect the alignment algorithm disclosed herein. Theraw bitmap image acquired from the camera may be used instead of theprocessed (e.g. jpeg) image. This raw image is typically storedseparately in the camera, for example in the “.rw2” format, and containsthe raw information captured by the camera sensor without anyprocessing.

After rotation is corrected, the image may be delimited to the lowestand highest x and y values of the coordinates of the pixels inside therecognized rectangular box. This image is denoted by I (x, y).Meanwhile, the mask for the image is calculated as M (x, y). This maskis a binary vector with the same dimensions as I (x, y) with the value‘0’ indicating the corresponding pixel in I (x, y) to be masked out fromthe Hamming distance computation. In general, two categories of pixelsmay be chosen to be masked out in certain examples of the presentdisclosure. The first is the pixels with the intensity greater than thethreshold computed by the Otsu method (for example, see the abovereference) and not considered as “scattered noise” in the borderrecognition phase. These include the printed rectangle, the filledsquare inside the box and any artefacts such as random pen scribbling.The second is the pixels outside the recognized box including all theedges in the picture. See the last diagram in FIG. 2 for anillustration. These pixels may be considered to contain unreliableinformation. They are identified as ‘0’ in a binary mask vector (similarto the identification of eyelids and eyelashes in iris recognition, forexample as described in John Daugman. 2003. The importance of beingrandom: statistical principles of iris recognition. Pattern Recognition36, 2 (2003), 279-291. Biometrics, the entire contents of which areincorporated herein by reference) and may be excluded in the subsequentHamming distance comparison process.

Gabor Filter

Gabor filters are typically used for edge detection in image processing.Besides, they have been found to perform efficiently in texturediscrimination. Gabor filters are able to extract both coherent andincoherent characteristics of textural patterns (for example, see JohnDaugman. 1993. High confidence visual recognition of persons by a testof statistical independence. Pattern Analysis and Machine Intelligence,IEEE Transactions on 15, 11 (November 1993), 1148-1161, the entirecontents of which are incorporated herein by reference). Coherentproperties are the patterns which remain unchanged between snapshots ofthe same sample while incoherent ones refer to the patterns which changebetween snapshots of different samples. The two dimensional Gaborwavelets are used in biometric recognition problems such as irisrecognition, fingerprint recognition and face recognition. A Gaborfilter's impulse response is basically that of a Gaussian filtermodulated by a sinusoidal wave. Consequently, Gabor filters capturefeatures in both the frequency and spatial domains. Generally speaking,a Gabor filter would consider the frequency of a pattern (“what”) aswell as the two-dimensional (2D) position of the pattern (“where”) (forexample, see the Daugman 1993 reference above). Let exp be the naturalexponential function. The 2D Gabor wavelet is calculated as followsusing Cartesian coordinates:

$\begin{matrix}{{{G\left( {x,y} \right)} = {\frac{f^{2}}{{\pi\eta}\; y} \cdot {\exp \left( \frac{{\eta^{2}x^{\prime 2}} + {\eta^{2}\; y^{\prime 2}}}{2\sigma^{2}} \right)} \cdot {\exp \left( {2\pi \; {ifx}^{\prime}} \right)}}}{{for}\mspace{14mu} x^{\prime}} = {{{x\; {\cos (\theta)}} + {y\; {\sin (\theta)}\mspace{14mu} {and}\mspace{14mu} y^{\prime}}} = {{{- x}\; {\sin (\theta)}} + {y\; {\cos (\theta)}}}}} & (2)\end{matrix}$

where f is the frequency of the sinusoidal wave, η and γ are constantfactors that together determine the spatial ellipticity of the Gaborwavelet, θ represents the orientation of the ellipticity, and σ is thestandard deviation of the Gaussian envelope.

Depending on the frequency of the sinusoidal wave and the orientation oftheir ellipticity, Gabor filters are capable of discriminating differenttextural characteristics. Usually, Gabor filters with a range ofdifferent frequencies, known as scales, and a range of differentorientations are applied to find out the best combination of scale andorientation for a specific texture analysis problem. For a fixed maximumfrequency f_(max) and a maximum of U scales, each scale index u definesthe frequency f used in Equation 2 as follows:

$\begin{matrix}{{{\forall{u \in \left\{ {1,2,\mspace{11mu} \ldots \mspace{14mu},U} \right\}}}:f} = \frac{f_{\max}}{{\sqrt{2}}^{u - 1}}} & (3)\end{matrix}$

For a maximum of V orientations, we consider V angles equallydistributed from 0 to π. Each orientation index v defines theorientation θ used in Equation 2 as follows:

$\begin{matrix}{{{\forall{\upsilon \in \left\{ {1,2,\mspace{11mu} \ldots \mspace{14mu},V} \right\}}}:\theta} = {\frac{\upsilon - 1}{V}\pi}} & (4)\end{matrix}$

A Gabor filter is applied to grey-scale images. Let I (x, y) representthe grey-scale image using Cartesian coordinates. The result of theapplication of Gabor filter G(x, y) is simply the 2D convolution of Iand G as follows:

C(x,y)=I(x,y)*G(x,y)=∫∫I(x,y)G(x−η,y−ξ)dηdξ

The result C (x, y) is a complex number for each x and y. C (x, y) canbe alternatively viewed as a matrix with the discrete values of x and ymapped to the columns and rows. Throughout the paper, functions definedover Cartesian coordinates and matrices are used interchangeably.

Fingerprint Generation

A fingerprint generation method according to an example of the presentdisclosure takes the output of a Gabor filter and produces a binarystring. Let the element located in row j and column k of the matrix C(x, y) be m_(jk)=a+bi. A 2-bit Gray code is defined based on whichquarter of the complex plane the element m_(jk)=a+bi falls in (see FIG.3). For example, when a and b are both positive, the encoded value willbe 11. Thus, every element in the matrix is replaced by two bits. Theresult is a binary string which may be referred to as the paperfingerprint.

Fractional Hamming Distance

After paper fingerprints are generated, fractional Hamming distancebetween any two fingerprints can be used to compare them. Hammingdistance is simply the number of positions in which the bits disagreebetween two fingerprints. This is a classical bit error rate (BER)metric in communication. Fractional Hamming distance is the normalizedversion, resulting a value between 0 and 1. Masking may be used todiscard the effect of irrelevant bits in a fingerprint. For eachfingerprint, a mask is defined as a binary string of the same length inwhich bits corresponding irrelevant positions are set to 0 and bitscorresponding effective positions are set to 1. The masks are calculatedin the preparation phase as discussed above. Given two fingerprints f₁and f₂, and their corresponding masks m₁ and m₂, the fractional Hammingdistance is calculated as follows:

$\begin{matrix}{{{HD}\left( {f_{1},f_{2},m_{1},m_{2}} \right)} = \frac{{{\left( {f_{1} \oplus f_{2}} \right)\bigcap m_{1}\bigcap m_{2}}}}{{{m_{1}\bigcap m_{2}}}}} & (5)\end{matrix}$

where ⊕ denotes the bitwise exclusive-OR (XOR) operation and ∩ denotesthe bitwise AND operation. A relatively small fractional Hammingdistance indicates that the two fingerprints are likely to belong to thesame paper sheet, while a relatively large fractional Hamming distance(for example, around 0.5) indicates that the two fingerprints are likelyto belong to different paper sheets. In the following, the expressionHamming distance (or HD for short) is used to refer to fractionalHamming distance.

Evaluation

In order to evaluate the above method for paper fingerprinting, severaldatasets may be collected in different situations. In the following, theparameter settings and configurations of an exemplary implementationunder which the evaluations may be carried out are first explained.Then, the details of the evaluation framework that may be used to assessthe results are provided. In particular, metrics used for evaluating theeffectiveness of biometric systems as well as those used for evaluatingthe effectiveness of physical unclonable functions (PUFs) may beconsidered, since paper fingerprints can be seen as both. Subsequently,results are given that justify certain choices in terms of how thedatasets are collected and the settings used for the Gabor filter.Finally, the details of the main dataset collection are given and theresults are provided, including evaluation of the method againstbiometric and PUF metrics.

Parameter Settings and Configurations

In order to obtain consistent fingerprints, a relatively small but fixedpart of a sheet of paper may be used as a source of fingerprintextraction. A rectangular box (e.g. 37 mm×57 mm) may be printed on thesheet to indicate this area. In addition, a small filled square (5 mm×5mm) may be printed in a corner (e.g. at the bottom left) of the box (seeFIG. 10). Using this small square, in the preparation phase the methodcan check that the rotation has been carried out correctly(distinguishing cases when the paper is placed upside-down or flipped).

In an exemplary implementation, the original photos may be 3456×4608pixels, for example. After the preparation phase, a corrected anddelimited image of variable size may be obtained, ranging between around2300×3300 pixels to 2350×3350 pixels, for example. This image may thenbe resized, for example to a 640×640 pixel image/which is then given asinput to the Gabor filter. The rectangular size conversion is for theconvenience of applying Gabor wavelets in the next stage to produce, forexample 2048 bits in the output (the same size as an iris code). A Gaborimpulse response of, for example size 100×100 may be used, and theoutput of Gabor filter, C, may be a complex matrix of, for example size640×640. This matrix may be downsampled to one of size 32×32, forexample, before being given as input to the fingerprint generationalgorithm. This downsampling process is done by simply picking theelements in, for example every 20th row and 20th column. Fingerprintgeneration replaces each complex value with, for example two bits.Hence, the final paper fingerprint is a string of size 2×32×32=2048 bitsin this example.

The output of the Gabor filter may be downsampled for two reasons.First, it makes the data storage more compact. With 2048 bits (256bytes), the fingerprint may be stored in a QR code as part of anauthentication protocol (explained in more detail below). Second,adjacent pixels in the image are usually highly correlated. Hence,downsampling serves to break the correlation between bits. This simpledownsampling technique can be effective to produce reliable and uniquefingerprints.

In an exemplary implementation, images may be captured, for example by aPanasonic DMC-FZ72 camera with a resolution of 16.1 Mega-pixels. Thistype of camera may be chosen for two main reasons: the ability tocapture a photo in macro mode from a short distance (e.g. minimum 1 cmfocus) and the ability to mount a macro flash ring over the lens.However, these characteristics are not unique to this specific cameraand many other cameras available in the market provide the samecharacteristics. An off-the-shelf common macro flash ring may be mountedon the camera lens, to maintain a constant distance between the lens andthe paper surface where the texture is photographed. The camera and itsaccessories in an exemplary implementation are shown in FIG. 4(a). Incertain examples, it is not necessary to use the flash of the macroflash ring; the light source may be an ordinary office overheadprojector as shown in FIG. 4(b). The light that the overhead projectorprovides is intense and adjustable. Furthermore, it has a flat surfacewith constant distance from the light source. This allows the paper tobe put on the surface and then the macro ring resting on top of itbefore the camera takes a photo of the paper texture. The use of themacro ring also serves to shield the effects of other ambient lightsources (e.g., daylight, office lighting). The effect of the lightsource by using an alternative source: for example a commodity light box(e.g. a tracing pad) as shown in FIG. 4(c), is discussed below.

Evaluations may be performed on a PC, for example with an Intel Corei7-2600S CPU @ 2.80 GHz with 8 GB of memory. The operating system maybe, for example 64-bit Windows 7 Enterprise. Matlab R2015a (64-bit) maybe used to implement the algorithms.

Evaluation Framework

The techniques disclosed herein may be regarded as related to the fieldsof biometrics and Physical Unclonable Functions (PUFs). Biometrics isthe science of authenticating humans by measuring their uniquecharacteristics and have a long history of research. A paper fingerprintworks similar to biometrics, except that it measures uniquecharacteristics of a physical object instead of a human being. Hence,common metrics that measure the error rate performance of a biometricsystem apply to the techniques described herein. On the other hand,paper fingerprints may be regarded as related to Physical UnclonableFunctions. Typically PUFs require a challenge and response dynamic, butaccording to a certain definition (for example disclosed in Roel Maes.2012. Physically unclonable functions: Constructions, properties andapplications. Ph.D. Dissertation. Katholieke Universiteit Leuven, theentire contents of which are incorporated herein by reference), papermay be regarded as a “non-intrinsic” PUF, i.e., a PUF that does notcontain the circuitry to produce the response on its own. Hence, thesame evaluation methods in PUF are also applicable to paperfingerprints.

Because of the relation to these two fields and their respectiveevaluation frameworks, an exemplary implementation according to thepresent disclosure may be evaluated based on metrics used in both fieldsfor a comprehensive analysis. Biometric or PUF metrics may be used.However, using both allows a meaningful comparison with relatedbiometrics and PUF systems to be performed. The relationships betweenthese metrics may be analyzed, and a unified framework may be definedthat can be applied to evaluate both biometric and PUF systems.

In the following a brief description of these metrics is given. There isdiscussed Hamming distance distributions, decidability, and recognitionrates including false rejection and false acceptance rates in the formercategory of metrics. In the latter category, uniformity and randomnessin the space dimension, reliability and steadiness in the timedimension, and uniqueness and bit aliasing in the device dimension areconsidered.

1) Biometric Metrics: A biometric authentication problem is a specificcase of a statistical decision problem in which one decides if two givenbiometric measurements belong to the same source or not. In order toprovide necessary information about the effectiveness of such abiometric, the parameters of the so-called biometric decision landscapeneed to be specified (for example, see John Daugman. 2000. Biometricdecision landscapes. Technical Report UCAM-CL-TR-482. University ofCambridge, the entire contents of which are incorporated herein byreference). If Hamming distance is used for comparison, as it is in thepresent example, the distributions of Hamming distance for two groups ofcomparisons need to be determined: for comparisons between paperfingerprints originating from the same paper sheet, and for comparisonsbetween paper fingerprints originating from different paper sheets.These are called same-group and different-group distributions,respectively.

For an effective biometric, the same-group and different-groupdistributions should be well-separated. This makes the decision problemsolvable. Let μ₁ and μ₂ denote the means, and σ₁ and σ₂ the standarddeviations of the two distributions. The decidability metric d′ may bedefined as follows:

$\begin{matrix}{d^{\prime} = \frac{{\mu_{1} - \mu_{2}}}{\sqrt{\frac{\sigma_{1}^{2} + \sigma_{2}^{2}}{2}}}} & (6)\end{matrix}$

where |⋅| denotes absolute value. Decidability as defined above isindicative of how well-separated the two distributions are: the furtherand the more concentrated the distributions are, the higher will thedecidability be. To give an idea about typical values, the decidabilityof iris recognition, a well-established and effective biometric method,is d′≈14 in an ideal measurement environment and d′≈7 in a non-idealenvironment (for example, see John Daugman. 2004. How iris recognitionworks. Circuits and Systems for Video Technology, IEEE Trans-actions on14, 1 (2004), 21-30, the entire contents of which are incorporatedherein by reference).

After determining the same-group and different-group distributions, onedecides a threshold value situated between the two distributions.Subsequently, the decision on whether two reported biometrics belong tothe same origin or not is then made by computing the Hamming distancebetween the two biometric samples and comparing it to the threshold. Foran effective biometric, measurements from the same origin haverelatively low Hamming distance and hence fall below the threshold,whereas measurements from different origins have relatively high Hammingdistance and fall above the threshold. If the distributions arecompletely separated, the decision is correct all the time. However inpractice usually there is some overlap between the two distributions.The proportion of biometrics from different origins falsely accepted asbeing from the same origin is known as the false acceptance rate (FAR).The proportion of biometrics from the same origin falsely rejected asbeing from different origins is known as the false rejection rate (FRR).For an effective biometric FAR and FRR should be low—ideally zero.

A widely used measure of effectiveness of a biometric is degrees offreedom (DoF). DoF is a measure of the combinatorial complexity of thebiometric test, or in other words the number of bits in a biometricmeasurement that are independent (for example, see the Daugman 2004reference above). Consider a biometric that provides degrees of freedomN, that is, N independent and unpredictable bits. A comparison betweentwo such biometrics from different origins can be modelled as theprobability that a threshold number of N independently chosen bitsagree. Hence, the different-group distribution for such a biometricwould follow the binomial distribution with mean μ=p and varianceσ²=Np(1−p), where p is the probability of single bit agreement. Hence,the degrees of freedom for a biometric with a different-groupdistribution that follows a binomial distribution with mean μ andvariance σ² can be calculated as follows:

$\begin{matrix}{N = \frac{\mu \left( {1 - \mu} \right)}{\sigma^{2}}} & (7)\end{matrix}$

2) PUF Metrics: Paper fingerprinting can be seen as an optical physicalunclonable function (PUF). Evaluating results against established PUFmetrics provides further information about the effectiveness of thetechniques described herein.

Herein, a unified framework is followed, which provides metrics toevaluate a PUF in three dimensions: space, time, and device (forexample, see Abhranil Maiti, Vikash Gunreddy, and Patrick Schaumont.2013. A systematic method to evaluate and compare the performance ofphysical unclonable functions. In Embedded systems design with FPGAs.Springer, 245-267, the entire contents are incorporated herein byreference). In the techniques described herein, PUFs are the paperfingerprints, and devices are the different paper sheets. Each of thesedimensions quantifies a specific quality of a fingerprint: the spacedimension analyses the overall variations of fingerprints, the timedimension indicates same-group consistency, and the device dimensiondiscusses the different-group diversity of fingerprints.

Before describing these dimensions, the symbols used in this frame-workare defined. Here we consider effective fingerprints, denoted by r. Theeffective fingerprint is the result of applying the appropriate maskover the original fingerprint f. The following parameters are used: L isthe number of bits in each fingerprint (2048 in one example). T refersto the number of samples taken from each paper sheet in a dataset (e.g.,in an exemplary benchmark dataset T=10). N is the total number of papersheets involved in a dataset (e.g., in an exemplary benchmark datasetN=100). The following indices may be used accordingly: n denotes thepaper sheet number within different sheets, t represents the samplenumber within the samples from the same paper sheet, and I shows I-thbit in the effective fingerprint.

Space Dimension. This dimension is concerned with bit variations withrespect to the locations of the bits in fingerprints. Metrics in thisdimension evaluate the overall inter-sheet behaviour of fingerprints.

Uniformity: This metric shows how uniform 0s and 1s are in afingerprint. The ideal value for this metric is 0.5. Uniformity of thefingerprint from the t-th sample and n-th sheet is calculated asfollows:

$\begin{matrix}{{{Uniformity}\left( {n,t} \right)} = {\frac{1}{L}{\sum\limits_{l = 1}^{L}\; r_{n,t,l}}}} & (8)\end{matrix}$

Randomness: This metric indicates the average randomness of the bits inthe fingerprints generated from several acquisitions from a sheet. Theideal value for this metric is 1. Randomness of the fingerprint bitsgenerated from the n-th sheet is calculated as follows:

$\begin{matrix}{{{{Randomness}\; (n)} = {{- \log_{2}}{\max \left( {p_{n},{1 - p_{n}}} \right)}}},{{{where}\mspace{14mu} p_{n}} = {\frac{1}{TL}{\sum\limits_{t = 1}^{T}\; {\sum\limits_{l = 1}^{L}\; r_{n,t,l}}}}}} & (9)\end{matrix}$

Time Dimension. This dimension is concerned with fingerprint variationswithin multiple samples. Metrics in this dimension evaluate the overallintra-sheet persistence of fingerprints within multiple samples.

Reliability: This metric shows how consistently fingerprints arereproduced by the same sheet. The ideal value for this metric is 1.Reliability of the fingerprints generated from the n-th sheet iscalculated as follows:

$\begin{matrix}{{{Reliability}(n)} = {1 - {\frac{2}{{T\left( {T - 1} \right)}L}{\sum\limits_{t_{1} = 1}^{T - 1}\; {\sum\limits_{t_{2} = {t_{1} + 1}}^{T}\; {\sum\limits_{l = 1}^{L}\; \left( {r_{n,t_{1},l} \oplus r_{n,t_{2},l}} \right)}}}}}} & (10)\end{matrix}$

Steadiness: This metric indicates the bias of individual fingerprintbits on average for a sheet. The ideal value for this metric is 1.Steadiness of the fingerprints generated from the n-th sheet iscalculated as follows:

$\begin{matrix}{{{{Steadiness}(n)} = {1 + {\frac{1}{L}{\sum\limits_{l = 1}^{L}\; {\log_{2}{\max \left( {p_{n,l},{1 - p_{n,l}}} \right)}}}}}}{{{where}\mspace{14mu} p_{n,l}} = {\frac{1}{T}{\sum\limits_{t = 1}^{T}\; r_{n,t,l}}}}} & (11)\end{matrix}$

Device Dimension. This dimension is concerned with fingerprintvariations between multiple sheets. Metrics in this dimension evaluatethe overall inter-sheet distinguishability of fingerprints.

Uniqueness: This metric represents how distinguishable a sheet is withina group of sheets. The ideal value for this metric is 0.5. Uniqueness ofthe fingerprints generated from the n-th sheet is calculated as follows:

$\begin{matrix}{{{Uniqueness}(n)} = {\frac{1}{T^{2}{L\left( {N - 1} \right)}} \cdot {\sum\limits_{t = 1}^{T}\; {\sum\limits_{{n^{\prime} = 1}{n^{\prime} \neq n}}^{N}\; {\sum\limits_{t^{\prime} = 1}^{T}\; {\sum\limits_{l = 1}^{L}\; \left( {r_{n,t,l} \oplus r_{n^{\prime},t^{\prime},l}} \right)}}}}}} & (12)\end{matrix}$

Aliasing: This metric indicates how likely different sheets are toproduce identical fingerprint bits. The ideal value for this metric is0.5. Bit-aliasing of the I-th bit of the fingerprints generated from adataset is calculated as follows:

$\begin{matrix}{{\text{Bit-Aliasing}(l)} = {\frac{1}{NT}{\sum\limits_{n = 1}^{N}\; {\sum\limits_{t = 1}^{T}\; r_{n,t,l}}}}} & (13)\end{matrix}$

Reflectance vs. Transmission

As discussed before, certain examples of the present disclosure capturepaper textural patterns and efficiently extract unique paperfingerprints from such patterns using a camera. By contrast, othertechniques extract paper fingerprints from the paper surface. In certainexamples of the present disclosure, textural patterns revealed by thetransmissive light typically contain richer features than the papersurface shown by the reflective light. To demonstrate this, thefollowing investigates the difference between the two patterns.

The paper photographing may be set up in two settings: one with thelight source on the same side of the paper and the other with the lightsource on the opposite side of the paper (see FIG. 5). In the former, anopaque object may be put behind the paper, so only the paper surface isphotographed based on the reflective light. 10 common A4 (210×297 mm)paper sheets with grammage 80 g/m² may be selected. 10 photos of eachsheet may be taken in each of the two settings. A common overheadprojector may be used as the light source. The effect of any ambientlight may be reduced by setting the data collection environment in adark room. This data collection results in two datasets: a 100-sampledataset (10 sheets with 10 samples for each sheet) for surfacemeasurements and a 100-sample dataset (10 sheets with 10 sample for eachsheet) for textural measurements.

After the data collection, the fingerprint extraction algorithm (asdiscussed above) may be performed for both datasets. FIG. 6 shows theHamming distance distributions for the two cases. Each diagram depictsfour distributions: for each case i.e., surface and texture, there isone curve, concentrated around lower values of Hamming distance, showingthe distribution of Hamming distance between pairs of fingerprints ofthe same paper sheet, and a second curve, concentrated around a Hammingdistance value of about 0.5, showing the distribution of Hammingdistance between pairs of fingerprints of different paper sheets.

Ideally, for effective fingerprint recognition, we want the “same-group”and “different-group” distributions to be as separate as possible, sincethen a threshold can easily be decided on and any two fingerprints witha Hamming distance below that threshold may be considered to belong tothe same paper sheet, and any two fingerprints with a Hamming distanceabove that threshold may be considered to belong to different papersheets.

As can be seen in FIG. 6, the two distributions, i.e., “same-group” and“different-group”, are well-separated in the case of texture, but lessso in the case of surface. In fact, in the case of texture, the minimumHamming distance for different comparisons is 0.46 and the maximumHamming distance for similar comparisons is 0.27, which shows that thereis no overlap between the two distributions. However, in the case ofsurface, the minimum Hamming distance for different comparisons is 0.44and the maximum Hamming distance for similar comparisons is 0.48, whichshows that there is some overlap between the two distributions, andhence false negative or false positive decisions are inevitable in thiscase. Indeed, decidability for the case of texture is around 20, but forthe case of surface it is around 6. Furthermore, the number of degreesof freedom provided by the texture is slightly higher than that providedby the surface. These results support the view that the texturalmeasurements through transmissive light contain more distinctivefeatures than surface measurements based on reflective light, and hencecan be used as a more reliable source for paper fingerprinting.

In the above, a specific image capturing condition, in which only onesnapshot is taken, is used. However, a method that is based on taking asingle snapshot is easier and quicker than those that require multiplemeasurements.

Determining Gabor Scale and Orientation

As discussed, Gabor filter can be configured with different scales andorientations. To find out the appropriate combination of scales andorientation for our method, we set up an initial experiment. Wecollected a dataset including two sub-datasets: the first one includes20 samples from one paper sheet; the second one includes one sample fromeach of 20 paper sheets. These two sub-datasets constitute oursame-group and different-group data, respectively. We applied Gaborfilter for 8 orientations, indexed from 1 to 8, representing angles 0,π/8, π/4, 3π/8, π/2, 5π/8, 3π/4, and 7π/8. Considering f_(max)=0.25, wealso considered multiple scales, indexed by integer values starting fromscale 1. We used fixed values of η=γ=√2 and σ=1.

Preferably, the different-group distribution should be centred around0.5 or a mean very close to 0.5. For scales greater than 7, the mean ofthe different-group distribution falls below 0.45, which indicatesundesirable bias on the binomial distributions (i.e., “tossing a coin”is no longer random in the a Bernoulli trial). Therefore, in thefollowing the scope of the investigation is limited to scales from 1 to7.

Calculations show that as the scale increases, the decidability of thedistributions increases, but at the same time the number of the degreesof freedom the different-group distribution provides decreases. This isbecause the scale relates to the spatial frequency components of theGabor filer—the smaller the scale is, the more detailed the featureextraction is. When the scale is one, the finest detail of the papertexture is extracted, which leads to high degrees of freedom in thegenerated fingerprint. However, at this scale, the image processing isextremely sensitive to noise, which reduces the separation between thesame-group and different-group histograms of Hamming distances.Increasing the scale results in a zooming-out effect. More correlationsbetween bits are introduced, which reduces the degrees of freedom. Buton the other hand, the feature extraction is more tolerant of noise. Asa result, the same-paper and different-paper characteristics become moredistinctive, which leads to a higher decidability.

The results for decidability and degrees of freedom for orientations 1to 8 and scales 1 to 7 are shown in FIGS. 7(a) and 7(b), respectively.Both figures also include a spline interpolation of average values ofdifferent orientation results within each scale to highlight thedominant trends. Therefore, there is an evident trade-off in choosingthe scale and orientation. Too low a scale would not provide anacceptable decidability, while too high a scale would not provide areasonable degree of freedom. Through experiments, it has been foundthat the combination of scale 5 and orientation 7 provides a goodtrade-off between decidability and degrees of freedom. As explainedlater, this combination provides nearly perfect recognition rates. Inthe following, findings based on this specific configuration of Gaborfilter are described.

The Benchmark Dataset

The main dataset on which the evaluations are reported is a set of 1000samples collected by taking 10 photos of each of 100 different papersheets to provide a good diversity. Typical office paper sheets are usedof size A4 (210 mm×297 mm) with grammage of 80 g/m². All the sheets werefrom the same pack with the same brand. In all of the photos, camerasettings including aperture and exposure time were kept constant. It wasattempted to keep the paper sheets visually aligned for the differentsamples, and separate experiments were conducted to evaluate therobustness of our algorithm against rotations (which are discussed belowSection 5). The main dataset collected here under relatively stableconditions are referred to as the benchmark dataset.

Experiment Results

In the following, results are presented of experiments reporting themetrics described above. Also presented are the timing measurements forthe method and a short discussion is provided on its practicality.Comparisons are provided with existing techniques whenever the relevantmetrics are reported in the literature.

Biometric metrics. The Hamming distance was calculated for allcomparisons, consisting of same-group comparisons and different-groupcomparisons. There are a total of ₁₀₀₀C₂=499,500 comparisons, of which100·₁₀C₂=4,500 are same-group comparisons and (1000×990)/2=495,000 aredifferent-group comparisons. FIG. 8 shows the distributions for thesame-group and different-group Hamming distance values. Clearly, the twodistributions are well-separated, which shows the effectiveness of thepaper fingerprinting method according to examples of the presentdisclosure. Indeed, the maximum same-group Hamming distance is 0.24,whereas the minimum different-group Hamming distance is 0.42, whichshows that there is no overlap between the two distributions. Hence, anythreshold between the above values would give FAR and FRR of zero. As anexample, the threshold can be chosen to be 0.4, but this is adjustable.Detailed error rate performance will be described below.

Decidability for the dataset is d′≈21, which compares favourably tod′≈14 for iris recognition in the ideal condition (see the Daugman 2003reference above). The number of degrees of freedom is calculated basedon Equation 7 as N=807, which means the entropy of the extractedfingerprints is 807 bits out of a total of 2048 bits. As compared to the249 degrees of freedom for iris (which has the same size of 2048 bits),the fingerprint in our case is more unique and contains less redundancy.FIG. 9 shows the histogram of same-group Hamming distance values on theleft and the distribution of different-group Hamming distance values onthe right. The diagram on the right also includes a binomialdistribution curve with degrees of freedom N=807, mean μ=0.495, andstandard deviation σ=0.018. Evidently, the different-group distributionclosely follows the binomial distribution.

PUF evaluations results. The PUF metrics results on the benchmarkdataset are shown in Table II under the column labelled “BenchmarkDataset”. It can be seen that in all metrics our dataset performed closeto ideal values. For comparison, we also included in Table II the PUFmetrics for two typical PUFs: Arbiter PUF, and Ring Oscillator PUF (forexample, see Abhranil Maiti, Vikash Gunreddy, and Patrick Schaumont.2013. A systematic method to evaluate and compare the performance ofphysical unclonable functions. In Embedded systems design with FPGAs.Springer, 245-267, the entire contents of which are incorporated hereinby reference). This shows that our method provides fingerprints withgood uniformity, randomness, reliability, steadiness, uniqueness, andbit-aliasing.

Timing Results & Usability. An exemplary implementation of the paperfingerprinting method described herein takes 1.30 seconds on average toprepare the photo, analyse the texture, and generate the fingerprint ona PC. This is reasonably fast. This is in contrast with other methods,which require four scans in different directions and then constructing a3D surface model. 3D modeling is generally considered a computationallyexpensive task.

The whole process of paper fingerprinting in an exemplary implementationof the method described herein is automatized and only requires a userto place the sheet of paper on the flat surface of the light source(e.g. overhead projector) and click a button to take a photo (e.g. by afixed camera). The example illustrated in FIG. 4 may be regarded as aproof-of-concept prototype to demonstrate the feasibility of extractingthe fingerprint based on the textural patterns. Other implementationsmay be improved, for example by tighter integration of various equipmentcomponents. For example, at a border control, when the official swipes apage in the passenger's passport through a slot, the slot may have theembedded light source on one side and a camera on the other side. Whenthe page is in the slot, a unique fingerprint can be extracted. Thefingerprinting area and orientation will be relatively fixed as it isdetermined by the dimensions of the slot. By comparing the extractedfingerprint with a reference sample (e.g., stored in the back-endsystem), the computer program can quickly determine if the passport pageis genuine. Further details on how to utilize the unique paperfingerprint in authentication protocols are described below.

TABLE I False recognition rates of all datasets considering a fractionalHD threshold of 0.4 Bench- Ideal mark Crum- Scrib- Heat- Mixed RateValue Dataset Rotated pled bled Soaked ed Light FAR 0% 0%   0%   0% 0%0% 0% 0% FRR 0% 0% 0.32% 3.2% 0% 0% 0% 0%

TABLE II PUF metrics for all datasets and two typical PUFs Arbiter RingPUF (APUF) Oscillator Ideal [Maiti PUF [Maiti Benchmark PUF MetricsValue et al. 2013] et al. 2013] Dataset Average Uniformity 0.5 0.5560.505 0.466 Average Randomness 1.0 0.846 0.968 0.907 Average Reliability1.0 0.997 0.991 0.945 Average Steadiness 1.0 0.984 0.985 0.938 AverageUniqueness 0.5 0.072 0.472 0.465 Average Bit Aliasing 0.5 0.195 0.5050.466

TABLE III Impact of Robustness Experiments on PUF metrics Bench- PUFIdeal mark Mixed Metrics Value Dataset Rotated Crumpled Scribbled SoakedHeat Light Average Uniformity 0.5 0.466 0.466 0.463 0.454 0.460 0.4600.466 Average Randomness 1.0 0.907 0.906 0.896 0.873 0.877 0.890 0.907Average Reliability 1.0 0.945 0.877 0.852 0.856 0.750 0.882 0.905Average Steadiness 1.0 0.938 0.839 0.528 0.870 0.554 0.554 0.874 AverageUniqueness 0.5 0.465 0.465 0.470 0.468 0.463 0.461 0.465 Average BitAliasing 0.5 0.466 0.466 0.463 0.454 0.460 0.460 0.466

Robustness Evaluations

In the following, an exemplary implementation is evaluated with respectto robustness in non-ideal circumstances. First, the robustness of themethod against misalignment is considered, i.e., in cases where therectangular box is not aligned to the photo frame. Then, the robustnessof the method against paper being roughly handled is considered in thefollowing cases: the paper sheet is crumpled, some scribbling is done inthe rectangular box, the sheet is soaked in water and dried afterwards,and the sheet is ironed after soaking and partially burnt. Finally, theeffect of using an alternative light source is considered. In thefollowing, the details of each experiment are given and the biometricand PUF metrics in each of the cases is provided.

Impact of Non-Ideal Data Collection

Photo Rotation. The orientation of the photo is the angle between therectangular box and the photo frame. A rotated photo is shown in FIG.10(b). In this example, the maximum rotation possible such that the boxis still fully captured within the boundary of the photo frame is around12°. 10 paper sheets have been selected and 5 samples collected in eachangle within {−12°, −11°, . . . , 0°, . . . , +11°, +12° }. This gives125 samples per sheet, 1250 samples in total.

FIG. 11 shows the Hamming distance distributions. As expected, thesame-group and different-group distributions get slightly closer to eachother in comparison with the benchmark dataset. However, decidability,although reduced, is still a healthy d′≈8. This shows that the imageprocessing method is somewhat sensitive to the image rotation. However,with the current method and based on a threshold of 0.4, the FAR isstill 0%, and the FRR is less than 1%. These values can be found inTable I.

The PUF metrics are presented in Table II. The experiment dataset stillhas good uniformity, randomness, and bit-aliasing, but there is a slightdrop in reliability, steadiness, and uniqueness compared to thebenchmark dataset.

The experiment shows that a method according to examples of the presentdisclosure is robust against non-ideal data collection in terms ofrotation. In comparison some other techniques require precise alignmentof each surface point across all scans.

Impact of Non-Ideal Paper Handling

In the following, an exemplary implementation is evaluated with respectto robustness against rough handling of paper sheet including crumpling,scribbling, soaking, and heating. For each of the experiments in thissection, a set of 10 paper sheets are selected. For each paper sheet, 5samples were taken before and 5 samples after the non-ideal handling ofthe paper sheet, adding up to a total of 100 samples per experiment. Thesame-group and different-group distributions under the test conditionsof crumpling, scribbling, soaking and heating are shown in FIG. 11. Forreadability, fitted curves are shown for the distributions. These curvesare non-parametric fits with a threshold bandwidth of 0.02 (i.e., thedistributions are merely smoothed).

Crumpling. In this experiment, the paper sheets were crumpled to theextent that the borders of the rectangular box were visibly distorted.It was not attempted to smooth out the sheet surface after crumpling. Anexample of a photo taken from a crumpled paper sheet can be seen in FIG.10(c).

The resulting Hamming distance distributions are shown in FIG. 11.Decidability is d′≈4.6. Based on the threshold of 0.4, the FAR is still0%, and the FRR is 3.2%. These values can be found in Table I.

The PUF metrics are presented in Table III. The experiment dataset stillhas good uniformity, randomness, and bit-aliasing, but there is a slightdrop in reliability and uniqueness and a bigger drop in steadinesscompared to the benchmark dataset.

Scribbling. In this experiment, random patterns were drawn with a blackpen over all samples such that each pattern covers around 5% of the boxarea. An example of such scribbling can be seen in FIG. 10(d). Thepreprocessing phase successfully identifies the scribbled area in themask in all samples.

The resulting Hamming distance distributions are shown in FIG. 11. Themaximum same-group Hamming distance is 0.25 and the minimumdifferent-group Hamming distance is 0.45. The distributions arewell-separated. Decidability is d′≈9.7. Based on the threshold of 0.4,the FAR is still 0%, and the FRR is also 0%. These values can be foundin Table I.

The PUF metrics are presented in Table III. The experiment dataset stillhas good uniformity, randomness, and bit-aliasing, but there is a slightdrop in reliability, steadiness, and uniqueness compared to thebenchmark dataset.

Soaking. In this experiment, the paper sheets were submerged in tapwater for around 20 seconds. Then, they were allowed to dry naturally,and the after-soaking samples were collected from the dried sheets.

The resulting Hamming distance distributions are shown in FIG. 11. Themaximum same-group Hamming distance is 0.36 and the minimumdifferent-group Hamming distance is 0.44. The distributions arewell-separated. Decidability is d′≈6.8. Based on the threshold of 0.4,the FAR is still 0%, and the FRR is also 0%. These values can be foundin Table I.

The PUF metrics are presented in Table III. The experiment dataset stillhas good uniformity, randomness, and bit-aliasing, but there is a slightdrop in reliability and uniqueness and a bigger drop in steadinesscompared to the benchmark dataset.

Heating. In this experiment, all the papers from the soaking experimentwere ironed for at least 20 seconds, to the extent that in some casesthere was a clearly visible colour change (to light brown) and the paperwas partly burnt.

The resulting Hamming distance distributions are shown in FIG. 11. Themaximum same-group Hamming distance is 0.30 and the minimumdifferent-group Hamming distance is 0.44. The distributions arewell-separated. Decidability is d′≈8.6. Based on the threshold of 0.4,the FAR is still 0%, and the FRR is also 0%. These values can be foundin Table I.

The PUF metrics are presented in Table III. The experiment dataset stillhas good uniformity, randomness, and bit-aliasing, but there is a slightdrop in reliability and uniqueness and a bigger drop in steadinesscompared to the benchmark dataset.

Summary. Taking all the above results into consideration, it can be seenthat the method shows the strongest robustness against scribbling. Boththe biometric and PUF measures support this observation. The Hammingdistance distributions are well-separated and all PUF metrics remainclose to ideal values. Fingerprinting is also fairly robust againstrotation, soaking, and heating. There is no or negligible falserejection rates and all PUF metrics possibly except for steadinessremain close to ideal values. Crumpling seems to pose the strongestchallenge to robustness. Although false rejection rate is 3.2% andsteadiness is not ideal, the method is still able to provide 0% falseacceptance rate and healthy PUF metrics otherwise.

Focusing on biometric metrics, authentication rates remain perfect ornearly perfect under all robustness tests. This means the methodprovides a paper-based document authentication technique which is ableto cope with non-ideal sample collection and rough handling.

Focusing on PUF metrics, space and device dimension metrics stay closeto ideal values under all tests, which indicates that the quality offingerprint bits are still good and the sheets remain clearlydistinguishable from one another. Time dimension metrics remain close toideal values for rotation and scribbling, but steadiness and in somecases reliability drops as a result of crumpling, soaking, or heating.This is expected as crumpling, soaking, and heating physically changethe paper sheets.

Impact of a Different Light Source

The light source should be bright enough to reveal the texture patternsin a paper sheet. In one exemplary implementation, an overhead projectormay be used, although the equipment is relatively bulky and expensive.However examples of the present disclosure are robust against using adifferent light source. To investigate this robustness, a commoditylight box (tracing pad) was used (see FIG. 4(c)). Then, the same papersheets were used as in the benchmark dataset—excluding 10 paper sheetsthat were used in other robustness tests—to collect a new set of samplesusing the new light source. The same data collection procedure as beforewas followed.

Due to the difference in the light intensity, the camera setting needsto be adjusted. In particular, the exposure time was altered to 1/500seconds and F-stop altered to f/5. These values were automaticallyrecommended by the camera. The exposure time is the duration that theshutter takes to capture a photo and F-stop is the radius of the lensdiaphragm; both of them are inspired by the way human eyes react to alight source. These modifications in the camera setting were necessarybecause of the change in the intensity of the light source. The finaldataset included 900 captured images, 10 samples from each paper sheet.

FIG. 12(a) shows the Hamming distance distributions using the light box.The same-group and different-group distributions are well-separated fromeach other. Applying the biometric metrics, our analysis shows thedecidability d′≈24 and the number of the degrees of freedom DoF≈846,both slightly higher than those obtained with the overhead projector.Based on the threshold of 0.4, the FAR and FRR are still 0%. Thesevalues can be found in Table I.

The PUF metrics are presented in Table III. These experiment resultsshow that all PUF metrics are comparable to those obtained earlier inthe benchmark dataset.

FIG. 12(b) shows the Hamming distance distribution by combining thelight box and overhead projector datasets. The number of the degrees offreedom is roughly unchanged at DoF≈836. However, the same-group databecome noisier because of mixing two different light sources. Thedecidability drops to 10. Despite of the mix of different light sources,the same-group and different-group histograms are still clearlyseparated. The maximum Hamming distance for the same-group samples is0.31 while the minimum Hamming distance of the different-group is 0.42.

The experiment shows that the method is robust against different lightsources, as long as the camera settings are set correctly.

Authentication Protocols

The following provides an explanation of authentication protocols basedon the extracted paper fingerprint, and a discussion of their practicalperformance.

Trust Assumptions

The fingerprinting technique according to the present disclosure may beapplied in a range of applications, e.g., to prevent counterfeiting ofpaper currency, passports, certificates, contracts and officialreceipts. The secure use of the fingerprint is based on two assumptions.Both assumptions are generally required in biometrics and physicalunclonable functions (PUF) applications.

The first assumption is physical “unclonability”. For example, it isassumed that it is infeasible to physically clone a paper sheet with thesame paper texture. The paper texture is formed from randomlyinterleaved wooden particles, as a naturally occurring outcome of thepaper manufacturing process. This process cannot be preciselycontrolled. Repeating exactly the same process to produce the same papertexture is considered to be prohibitively expensive, if not impossible(for example, see Ravikanth S. Pappu. 2001. Physical one-way functions.Ph.D. Dissertation. Massachusetts Institute of Technology.http://pubs.media.mit.edu/pubs/papers/01.03.pappuphd.powf.pdf the entirecontents of which are incorporated herein by reference).

The second assumption is about a trustworthy measuring process. Take thehuman fingerprint authentication as an example. If an attacker is ableto deceive the scanner by presenting a gummy finger, the securityguarantee based on the “unclonability” assumption will be lost. In anybiometric or PUF application, it is important to ensure that themeasurement is performed on a real object and a fresh measurement isacquired. In practice, this is often realized through the humansupervision in the process or by using specialized equipment (e.g., irisscanners with embedded liveness test). In the case of paper documents,visual inspection can be applied to check that they are made of paperand the paper fiber texture has not been tampered with. An attacker maytry to interfere with the texture measurement by printing patterns onthe paper surface. Using today's commodity printers, it seems unlikelythat an attacker is able to print patterns that are precise at the pixellevel under the microscopic view of a high-resolution camera (since theprint head cannot be precisely controlled and each printed dot tends tobe in a scattered pattern due to imperfection of the printing process;see William Clarkson, Tim Weyrich, Adam Finkelstein, Nadia Heninger, JAlex Halderman, and Edward W Felten. 2009. Fingerprinting blank paperusing commodity scanners. In Security and Privacy, 2009 30th IEEESymposium on. IEEE, 301-314, the entire contents of which areincorporated herein by reference). However, when the measurement is notguaranteed to be coming from real paper texture, the acquisition processis no longer trustworthy—an attacker can at least deny theauthentication by printing random patterns with strong contrast on thepaper. This threat can be addressed by checking that the intended areafor authentication is free from overprinting.

Comparison Based on Hamming Distance

A straightforward application of authenticating a paper fingerprint isbased on comparing the Hamming distance between two fingerprints. Itconsists of two phases. In the first phase, a paper fingerprint, alongwith a mask, is extracted from the textural patterns as the template andstored in a database. In the second phase, given a provided paper sheet,the same fingerprinting algorithm is followed to output a newfingerprint and a mask. Depending on the applications, there are twotypes of authentication modes: verification or recognition.

Verification works on a one-to-one comparison. This assumes thereference to the stored template is known (as it is often provided bythe authenticating subject). Hence, once the template is retrieved, itis a straightforward comparison between two fingerprints based on theirHamming distance as explained in Equation 5. This comparison determinesif the presented paper sheet is the same as the one registered earlier.

By contrast, recognition works on a one-to-many comparison. In thiscase, the reference to the pre-stored template is unknown. Hence, theprogram searches throughout the database, comparing the extractedfingerprint exhaustively with each of the stored templates in orderidentify a match where the Hamming distance is sufficiently small.

In terms of accuracy, the recognition mode is generally more demandingthan the verification mode, because the false accept rate accumulateswith the size of the database. As an illustration, let P₁ be the falseacceptance rate for one-to-one matching in the verification mode. AssumeP₁ is very small. Let P_(n) be the false acceptance rate in therecognition mode for a database of n records.

P _(n)=1−(1−P ₁)^(n) ≈n·P ₁

The above equation shows that the accumulative false acceptance rate inthe one-to-many mode increases roughly linearly with the size of thedatabase (see the Daugman 2003 reference above). Hence, for theone-to-many matching to work accurately, the false acceptance rate forthe one-to-one comparison must be extremely small.

For the paper fingerprints extracted in examples of the presentdisclosure, they have sufficient entropy to support precise recognitioneven for an extremely large database. Based on the binomialdistributions with 807 degrees of freedom, the false acceptance ratesfor comparing two paper fingerprints are listed in Table IV. If we optto maintain P_(n)<10⁻⁶ for the recognition mode as stated in the Daugman2003 reference above, an algorithm according to the present disclosurecan easily support searching a database of 3 quintillions (3×10¹⁸)fingerprints at a threshold of 0.32. By comparison, for the sameaccuracy (<10⁻⁶) and the same threshold (0.32), iris recognition canonly support a database of only 26 iris codes. As stated in the Daugman2003 reference above, for a database of a million iris codes, thethreshold needs to be adjusted downwards to below 0.27 to keep the falseaccept rate under 10⁻⁶. Because of the much higher degrees of freedom ofpaper fingerprints, they can be used for the recognition application ata much larger scale than the iris biometric.

TABLE IV False Acceptance Rate (FAR) for comparing two fingerprints HDThreshold False acceptance rate 0.30 7.1 × 10⁻³¹ 0.31 5.3 × 10⁻²⁸ 0.322.7 × 10⁻²⁵ 0.33 1.0 × 10⁻²² 0.34 2.5 × 10⁻²⁰ 0.35 4.5 × 10⁻¹⁸ 0.36 5.8× 10⁻¹⁶ 0.37 5.2 × 10⁻¹⁴ 0.38 3.3 × 10⁻¹² 0.39 1.5 × 10⁻¹⁰ 0.40 5.2 ×10⁻⁹ 

Paper Fingerprint Encryption

One limitation with the previous verification/recognition method is thatthe template is stored in plaintext in the database. When the plaintexttemplate is revealed, it may cause degradation of security. This isespecially the case with biometrics, since biometric data is consideredprivate to each individual. Paper fingerprints are essentially“biometrics” of paper. One technique in biometrics is through biometricencryption. A similar technique can be applied to realize fingerprintencryption. In the following, an exemplary implementation is described,and it is shown that because paper fingerprints have much higher entropythan even the most accurate biometric in use (iris), the correspondingencryption scheme is able to provide much higher security assurance aswell.

This exemplary implementation comprises two phases. In phase one, theprogram extracts a paper fingerprint from the paper texture as areference f_(a). It then generates a random key k (e.g. 140 bits), andexpands the key to a pseudo fingerprint f_(p)=ErrorCC(k) (e.g. a2048-bit codeword) where ErrorCC is an error-correction encoding scheme,for example based on Hadamard-Reed-Solomon. There may be a combinationof block and random errors in fingerprints obtained in examples of thepresent disclosure; therefore, a concatenated approach may be selected.The choice of 140 bits k is a balance between security (e.g. minimum 128bit security for the secret key) and performance, as well as consideringthe special parametric requirements for a concatenated code scheme towork at a desired level of error correction. Subsequently, the schemecomputes an encrypted fingerprint r=f_(a)⊕f_(p). In addition, theprogram computes h=H(k) where H is a secure one-way hash function.Finally, the program stores r and h in the database. Alternatively, rand h can be stored in a 2-D barcode printed on paper. The advantage ofdoing so is to allow authentication in the off-line mode. In this case,an additional digital signature s should be included to prove theauthenticity of data in the barcode. At this stage, the originaltemplate f_(a) and the random key k can be safely deleted. Theregistration process is summarized in Algorithm 1. FIG. 13 shows a QRcode generated from the registration phase in an example of the presentdisclosure.

The second phase is authentication. In this phase, data from the 2-Dbarcode is first read and the digital signature verified. A paperfingerprint f_(s) is extracted from the provided paper sheet. Theprogram then computes:

$\begin{matrix}\begin{matrix}{{f_{s} \oplus r} = {f_{s} \oplus \left( {f_{a} \oplus {{Error}\; {{CC}(k)}}} \right)}} \\{= {\left( {f_{e} \oplus f_{a}} \right) \oplus {{{Error}{CC}}(k)}}} \\{= {e \oplus {{{Error}{CC}}(k)}}}\end{matrix} & \;\end{matrix}$

In the above equation, e can be regarded as “noise” added to thecodeword ErrorCC(k). As explained above, the Hamming distances betweensame-paper fingerprints typically range from 0 to 0.25. In thedefinition of the Hadamard-Reed-Solomon code, in this example the codingparameters are the same as described in Feng Hao, Ross Anderson, andJohn Daugman. 2006. Combining crypto with biometrics effectively.Computers, IEEE Transactions on 55, 9 (2006), 1081-1088, the entirecontents of which are incorporated herein by reference. The resultanterror correction code is capable of correcting up to 27% error bits in a2048-bit codeword. Hence, by running the Hadamard-Reed-Solomon decodingscheme, the error vector e can be effectively removed, and the originalk can be recovered error-free. The correctness of the decoding processcan be verified by comparing the obtained k against the retrieved H(k).This authentication process is summarized in Algorithm 2.

ALGORITHM 1: Registration Generate Random key k ; Generate ReferencePaper Fingerprint f_(a); Expand key k to Pseudo Fingerprint f_(p) ;Calculate r = f_(a) ⊕ f_(p); Calculate h = H(k); Calculate DigitalSignature s = Sig(r,h); Store (r,h,s) in a 2-D barcode ;

  ALGORITHM 2: Verification Read r, h = H(k) and s = Sig(r, h) ; ifSignature Verification Success then  | Generate Paper Fingerprint f_(s);  | Calculate f′ = f_(s) ⊕ r ;  | Acquire k′ by decoding f′ ; | Calculate H(k′) ;  | if H(k′)==H/(k) then  | | Success ;  | else | | Failure ; else  | Failure ;

A key feature of the above “fingerprint encryption” scheme is that itpreserves the secrecy of the fingerprint template since it forms thebasis for authentication. In this way, no fingerprint template is storedin the plain form. As an example for comparison, without using thisencryption scheme, the barcode would contain the plain fingerprinttemplate. Once in the line of sight to an attacker, the barcode can betrivially read say by using a video camera, hence the template will bestolen. With the encryption scheme applied, the attacker would needphysical access to the paper in order to take a close-up snapshot of thefiber textures with a bright light source shining underneath the paper.This makes the attack significantly more difficult to carry out inpractice without the user noticing it.

Hence, the application of privacy preserving protocol for authenticationavoids storing the texture structure in the plain text form. The goalhere is to protect the paper texture from an attacker who does not havephysical access to the paper sheet itself. An adversary who has accessto the barcode printed on the paper can read all data including anencrypted fingerprint r=f_(a)⊕ErrorCC(k). One potential problem is thatif the fingerprint f_(a) contains significant correlations between bits,r may leak information about the fingerprint. The iris code may be givenas an example to illustrate that due to a high level of redundancy iniris codes, the encrypted iris code only has a lower-bound security of44 bits. However, 44 bits security is not sufficient to satisfy highsecurity requirements. As a result, the encrypted iris code (also calledthe secure sketch in the PUF literature) should not be published aspublic data; instead, it should be stored in a personal token.

The above limitation with the iris codes does not apply in examples ofthe present disclosure. Although the paper fingerprint in an exemplaryimplementation may have the same size as an iris code (e.g. 2048 bits),it has much higher degrees of freedom (e.g. 807 as compared to 249).Following the same sphere-packing bound as defined in the Hao 2006reference above, the lower-bound security for the encrypted fingerprintsmay be estimated as follows. Here, the lower-bound security refers tothe minimum efforts required for a successful brute-force attack, underthe assumption that the attacker has perfect knowledge of thecorrelations within the document paper sheet's fingerprint, hence theuncertainty (or entropy) about the fingerprint is 807 bits instead 2048bits. The error correction capability for the Hadamard-Reed-Solomon codeallows correcting up to 27% error bits. So in principle the attackeronly needs to guess a fingerprint that is within the Hamming distance of807×0.27≈218 bits to the correct fingerprint. Following the estimationmethod in the Hao 2006 reference above, based on the sphere-packingbound (see Richard W Hamming. 1950. Error detecting and error correctingcodes. Bell System technical journal 29, 2 (1950), 147-160, the contentsof which are incorporated herein by reference), the minimum guess effortwith z=807 and w=218 is calculated with the following equation:

$\begin{matrix}{{ \geq \frac{2^{z}}{\sum_{i = 0}^{w}\begin{pmatrix}z \\i\end{pmatrix}}} = 2^{133}} & (14)\end{matrix}$

The above bound states that an attacker with full knowledge aboutfingerprint correlations and the error correction process would need atleast 2¹³³ attempts in order to uncover the original fingerprint used inthe registration and the random key k. This 133-bit security is muchhigher than the 44-bit security reported in the Hao 2006 referenceabove, and is sufficient for almost all practical applications. This ispossible because the paper textural patterns are far more distinctivethan iris textural patterns. In iris, there exist substantialcorrelations along the radial structures. The same phenomenon does notexist in paper texture, which explains the higher degrees of freedom inexamples of the present disclosure. This high level of security makes itpossible to simply store the (r, h, s) values on a barcode instead of ina secure database. Alternatively, they may be stored in an RFID chip,and retrieved wirelessly during the verification phrase (e.g., in ane-passport application).

The performance of this authentication scheme may be evaluated based onthe benchmark database and the scheme is able to achieve perfect errorrates: 0% FRR and 0% FAR. Note that this performance evaluation isslightly different from the direct comparison between two fingerprintsbased on their Hamming distance. The authentication is successful, onlyif the Hadamard-Reed-Solomon code is able to correct the errors(introduced by the XOR between two fingerprints) added to the errorcorrection codeword, and hence recover the same random k (verified againH(k)). The authentication protocol may accommodate raw fingerprints,without masks. FIG. 14 shows the histogram of Hamming distance betweenraw fingerprints without masks. The same-paper and different-paperdistributions are well-separated. The error correct code implementedcorrects errors up to 27%. This is sufficient to correct errors for allsame-paper fingerprints, yet not sufficient for different-paperfingerprints. This explains the 0% FRR and 0% FAR that are obtained (seeFIG. 14).

Certain prior art paper-fingerprinting techniques have differentrequirements on paper material, use different types of illuminatingsources and scanning equipment, apply different signal processingtechniques and obtain fingerprints of different types and features.Examples of the present disclosure provide a practical solution thatworks with ordinary paper, may use an ordinary lighting source combinedwith an off-the-shelf camera, takes a relatively short time (e.g. only1.3 seconds) to produce a compact fingerprint (e.g. 256 bytes) from onesnapshot, may achieve an ideal 0% FFR, 0% FAR as well as very highentropy (807 bits) in fingerprints, and is demonstrably robust againstrotation, crumpling, scribbling, soaking and heating. The near perfectresult is attributed to the idea of capturing the paper texturalpatterns through transmissive light. As detailed above, usingtransmissive light reveals richer textural patterns than reflectivelight and produces more reliable features. This explains the superiorresults of examples of the present disclosure as compared to previoussurface-based paper fingerprinting methods.

Examples of the present disclosure fingerprint a paper sheet based onits texture patterns instead of features on the surface. The formercontain more distinctive features than the latter with higherdecidability in the histogram of Hamming distance distributions.Experiments may be set up to use a commodity camera to photograph thetexture patterns with a light source shining on the other side of thepaper. The rich texture patterns may be processed using Gabor waveletsto generate a compact, for example 2048-bit, fingerprint code. Based onthe collected database, zero error rates may be achieved. The methodworks well with different light sources, and is resistant againstvarious distortions such as crumpling, scribbling, soaking and heating.The extracted fingerprints may contain 807 degrees-of-freedom, forexample, which is sufficiently high for many practical applications. Asan example, some applications (like e-passport) rely on atamper-resistant RFID chip embedded in the paper document for provingthe authenticity of the document (through a challenge-response protocolbased on a long-term secret stored in the chip). A method according tothe present disclosure provides an alternative solution that leveragesthe natural physical properties of the paper document instead of thetamper resistance of an extra embedded chip.

Examples of the present disclosure may be applied to office papersheets. In addition, examples of the present disclosure may be appliedto other types of paper, such as thermal paper, labels and passportpages as long as the light can transmit through. Based on the thicknessof the paper and the difference in the texture materials, some changesin the intensity of the light, camera settings, Gabor filter scale andorientation may be required.

FIGS. 15 and 16 are respectively a flow chart of a method, and a blockdiagram of an apparatus, for preventing counterfeiting of an objectaccording to examples of the present disclosure (e.g. “registration”).

Referring to FIG. 15, in a first step 1501, an image of at least aportion of the object is captured. The portion of the object whose imageis captured is at least partially transparent, and the captured imageincludes features of the internal structure of the object. In certainexamples, the object comprises a piece of paper, and the internalstructure of the object comprises the texture of the paper resultingfrom the arrangement of fibres from which the paper is made. The imagemay be captured, for example, by illuminating one side of the objectusing any suitable type of light source, and capturing the image fromthe other side of the object using any suitable type of camera.

In certain examples, a designated area of the captured image may beidentified, and the captured image may be corrected for any rotationaland/or linear misalignment, for example in a manner described above. Incertain examples, the designated area may be indicated by a boundary,and a marker may be provided at a predetermined position relative to thedesignated area for indicating a correct orientation of the designatedarea. In certain examples, one or more artefacts in the captured imagemay be identified, and a mask for the image for masking the artefactsmay generated, for example in the manner described above.

In a next step 1503, a code is generated, based on the image, such thatthe code encodes features of the internal structure of the object. Incertain examples, the code may be generated by applying a filter to theimage to obtain a filtered image, and processing the filtered image toobtain a binary code. For example, the filter may be a Gabor filter orany other suitable type of filter or function, and when a Gabor filteris used the filtered image C(x, y) may be computed in the mannerdescribed above. In certain examples, the filtered image may beprocessed by applying a Gray code to the filtered image in the mannerdescribed above, or by applying any other suitable encoding scheme. Incertain examples, the binary code may be encrypted, for example in themanner described above or in any other suitable manner. For example, arandom key, k, may be generated, and then a codeword f_(p) may beobtained by applying any suitable type of error-correction encodingscheme (e.g. the Hadamard-Reed-Solomon code scheme), ErrorCC, to therandom key according to f_(p)=ErrorCC(k). An encrypted binary code, r,may then be computed according to r=f_(a)⊕f_(p), and a hash value, h,may be computed according to h=H(k).

In a next step 1505, the code is recorded (i.e. so that it can beretrieved later for the purpose of authentication). For example, thecode may be printed on the object (e.g. as a sequence of digits, or inthe form of a barcode or QR code and the like), or stored in a database,on a recording medium that is readable via short-range wirelesscommunication (e.g. an RFID tag and the like), or on an electronicallyreadable recording medium (e.g. a disc, memory chip and the like). Incertain examples, various values may be recorded. For example, thevalues r and h may be recorded. In certain examples, a digitalsignature, s, may be computed based on r and h, and the digitalsignature may also be recorded.

The method of FIG. 15 may be implemented in any suitable manner usingany suitable combination of hardware and/or software. One such exampleis an apparatus for preventing counterfeiting of an object asillustrated in FIG. 16. As illustrated, the apparatus 1600 comprises acamera 1601 for capturing an image of at least a portion of the object,a light source 1603 for illuminating the portion of the object whoseimage is captured, and a processor (or controller) 1605 for performingthe various operations and control required for implementing thetechniques described above, including generating, based on the image, acode that encodes features of the internal structure of the object, andoutputting the code. In certain examples, the apparatus 1600 may furthercomprise a guide and/or holder for assisting the user in guiding theobject to the correct position and/or holding the object in the correctposition for image capture.

FIGS. 17 and 18 are respectively a flow chart of a method, and a blockdiagram of an apparatus, for authenticating an object according toexamples of the present disclosure. (e.g. “verification”).

Referring to FIG. 17, in a first step 1701 an image of at least aportion of the object is captured. Step 1701 of FIG. 17 may be performedin substantially the same manner as step 1501 of FIG. 15. In particular,the portion of the object whose image is captured is at least partiallytransparent, and the captured image includes features of the internalstructure of the object. The portion of the object whose image iscaptured in step 1701 of FIG. 17 should correspond to the portion of theobject whose image is captured in step 1501 of FIG. 15.

As above, in certain examples, the object comprises a piece of paper,and the internal structure of the object comprises the texture of thepaper resulting from the arrangement of fibres from which the paper ismade. The image may be captured, for example, by illuminating one sideof the object using any suitable type of light source, and capturing theimage from the other side of the object using any suitable type ofcamera.

As above, in certain examples, a designated area of the captured imagemay be identified, and the captured image may be corrected for anyrotational and/or linear misalignment, for example in a manner describedabove. In certain examples, the designated area may be indicated by aboundary, and a marker may be provided at a predetermined positionrelative to the designated area for indicating a correct orientation ofthe designated area. In certain examples, one or more artefacts in thecaptured image may be identified, and a mask for the image for maskingthe artefacts may generated, for example in the manner described above.Alternatively or additionally, a predetermined mask (e.g. a maskdetermined during the method of FIG. 15) may be applied.

In a next step 1703, a code is generated, based on the image, such thatthe code encodes features of the internal structure of the object. Step1703 of FIG. 17 may be performed in a similar manner as step 1503 ofFIG. 15. For example, the code may be generated by applying a filter(e.g. a Gabor filter in a manner described above, or any other suitabletype of filter or function) to the image to obtain a filtered image, andprocessing the filtered image (e.g. by applying a Gray code to thefiltered image in the manner described above, or by applying any othersuitable type of encoding scheme) to obtain a binary code.

In a next step 1705, one or more reference values, comprising at least areference code, may be read. For example, the code may be read (e.g.optically) from a printed image (e.g. a sequence of digits, a barcode orQR code and the like) on the object, or retrieved from a database, froma recording medium that is readable via short-range wirelesscommunication (e.g. an RFID tag and the like), or from an electronicallyreadable recording medium (e.g. a disc, memory chip and the like).

In a next step 1707, the object may be authenticated based on the code,f_(s), and the reference code (e.g. corresponding to the encryptedbinary code, r, recorded in step 1505 of FIG. 15). In certain examples,the reference values further comprise a reference hash value(corresponding to the hash value, h, recorded in step 1505 of FIG. 15).In this case, the object may be authenticated by first computing acodeword f_(p)′ according to f_(p)′=f_(s)⊕r, then applying an errorcorrection code scheme (e.g. the Hadamard-Reed-Solomon code scheme) tothe codeword f_(p)′ to obtain a value k′, and the object may beauthenticated based on a comparison between a hash value H(k′) computedfrom the value k′ and the reference hash value h. The hash function, H,applied here to k′ may be the same as the hash function that was used tocompute h.

In certain examples, a digital signature, s, of the one or morereference values (corresponding to the signature, s, recorded in themethod of FIG. 15) may also be read, and the one or more referencevalues may be verified based on the digital signature. In certainexamples, steps 1701-1707 of FIG. 17 may be carried out only if theverification of the one or more reference values is successful.

The method of FIG. 17 may be implemented in any suitable manner usingany suitable combination of hardware and/or software. One such exampleis an apparatus for authenticating an object as illustrated in FIG. 18.As illustrated, the apparatus 1800 comprises a camera 1801 for capturingan image of at least a portion of the object, a light source 1803 forilluminating the portion of the object whose image is captured, a reader1805 for reading one or more reference values comprising at least areference code, and a processor (or controller) 1807 for performing thevarious operations and control required for implementing the techniquesdescribed above, including generating, based on the image, a code thatencodes features of the internal structure of the object, andauthenticating the object based on the code and the reference code.Similar to the apparatus of FIG. 16, in certain examples, the apparatus1800 of FIG. 18 may further comprise a guide and/or holder for assistingthe user in guiding the object to the correct position and/or holdingthe object in the correct position for image capture.

Although the use of a hash function has been described above, theskilled person will appreciate that any suitable one-way function may beused.

1. A method for preventing counterfeiting of an object, the methodcomprising: capturing an image of at least a portion of the object,wherein the portion of the object whose image is captured is at leastpartially transparent, and wherein the captured image includes featuresof the internal structure of the object; generating, based on the image,a code that encodes features of the internal structure of the object;and recording the code.
 2. The method according to claim 1, whereingenerating the code comprises: applying a filter to the image to obtaina filtered image; and processing the filtered image to obtain a binarycode.
 3. The method according to claim 2, wherein the filter is a Gaborfilter.
 4. The method according to claim 3, wherein the filtered imageC(x, y) is given by:C(x,y)=I(x,y)*G(x,y)=∫∫I(x,y)G(x−η,y−ξ)dηdξ where I(x, y) represent theimage in grey-scale using Cartesian coordinates, C(x, y) is a complexnumber for each x and y, * denotes convolution, and G(x, y) is the Gaborfilter defined by:$\mspace{20mu} {{G\left( {x,y} \right)} = {\frac{f^{2}}{{\pi\eta}\text{?}} \cdot {\exp \left( \frac{{\eta^{2}\text{?}} + {\text{?}y^{\prime 2}}}{2\sigma^{2}} \right)} \cdot {\exp \left( {\text{?}{fx}^{\prime}} \right)}}}$  for  x^(′) = x cos (θ) + y sin (θ)  and  y^(′) = −x sin (θ) + y cos (θ)?indicates text missing or illegible when filed where ¦ is thefrequency of the sinusoidal wave, η and γ are constant factors thattogether determine the spatial ellipticity of the Gabor wavelet, θrepresents the orientation of the ellipticity, and σ is the standarddeviation of the Gaussian envelope.
 5. The method according to claim 2,wherein processing the filtered image comprises applying a Gray code tothe filtered image.
 6. The method according to claim 5, wherein the Graycode is a two-bit Gray code for converting a complex number a+bi intotwo bits based on which quarter of the complex plane the complex numberfalls in, and wherein applying the Gray code comprises converting eachelement of the matrix C(x, y) into two bits according to the Gray code,wherein C(x, y) represents the filtered image.
 7. The method accordingto claim 2, further comprising encrypting the binary code, whereinrecording the code comprises recording the encrypted binary code.
 8. Themethod according to any of claim 2, further comprising: generating arandom key, k; obtaining a codeword ¦_(p) by applying anerror-correction encoding scheme, ErrorCC, to the random key accordingto ¦_(p)=ErrorCC(k), wherein ¦_(p) has the same size as the binary code¦_(a); computing an encrypted binary code, r, according to r=¦_(s)Å¦_(p), where Å denotes modulo-2 addition; and computing a hash value,h, according to h=H(k), where H is a one-way hash function, whereinrecording the code comprises recording the encrypted binary code r andthe hash value h.
 9. The method according to claim 8, further comprisingcomputing a digital signature, s, based on r and h, wherein recordingthe code comprises recording the digital signature, s.
 10. The methodaccording to claim 1, further comprising: identifying a designated areaof the captured image from which the code is generated; and correctingthe captured image for any rotational and/or linear misalignment. 11.The method according to claim 10, wherein the designated area isindicated by a boundary, and wherein a marker is provided at apredetermined position relative to the designated area for indicating acorrect orientation of the designated area.
 12. The method according toclaim 1, further comprising: identifying one or more artefacts in thecaptured image; and generating a mask for the image for masking theartefacts.
 13. The method according to claim 1, wherein capturing theimage comprises: illuminating one side of the object; and capturing theimage from the other side of the object.
 14. The method according toclaim 1, wherein recording the code comprises one or more of: printingthe code on the object; printing the code on the object in the form of abarcode or QR code; storing the code in a database; storing the code ona recording medium that is readable via short-range wirelesscommunication; and storing the code on an electronically readablerecording medium.
 15. The method according to claim 1, wherein theobject comprises paper, and wherein the internal structure of the objectcomprises the texture of the paper resulting from the arrangement offibres from which the paper is made.
 16. An apparatus for preventingcounterfeiting of an object, the apparatus comprising: a camera forcapturing an image of at least a portion of the object, wherein theportion of the object whose image is captured is at least partiallytransparent, and wherein the captured image includes features of theinternal structure of the object; a processor for generating, based onthe image, a code that encodes features of the internal structure of theobject, and outputting the code.
 17. The apparatus according to claim16, further comprising a light source for illuminating the portion ofthe object whose image is captured.
 18. A method for authenticating anobject, the method comprising: capturing an image of at least a portionof the object, wherein the portion of the object whose image is capturedis at least partially transparent, and wherein the captured imageincludes features of the internal structure of the object; generating,based on the image, a code that encodes features of the internalstructure of the object; reading one or more reference values comprisingat least a reference code; and authenticating the object based on thecode and the reference code.
 19. The method according to claim 18,wherein the reference values further comprise a reference hash value,and wherein authenticating the object comprises: computing a codeword¦_(p)¢ according to ¦_(p)¢=¦_(s) Å r, where ¦_(s) denotes the code, rdenotes the reference code, and Å denotes modulo-2 addition; applying anerror correction code scheme to the codeword ¦_(p)¢ to obtain a valuek¢; authenticating the object based on a comparison between a hash valuecomputed from the value k¢ and the reference hash value.
 20. The methodaccording to claim 18, further comprising verifying the one or morereference values based on a digital signature of the one or morereference values.
 21. An apparatus for authenticating an object, theapparatus comprising: a camera for capturing an image of at least aportion of the object, wherein the portion of the object whose image iscaptured is at least partially transparent, and wherein the capturedimage includes features of the internal structure of the object; areader for reading one or more reference values comprising at least areference code; a processor for generating, based on the image, a codethat encodes features of the internal structure of the object, andauthenticating the object based on the code and the reference code. 22.The apparatus according to claim 21, further comprising a light sourcefor illuminating the portion of the object whose image is captured.